# Pilates is a popular set of exercises for the treatment of individuals with lower back pain. The method has six basic principles: centering, concentration, control, precision, flow, and breathing. The article “Efficacy of the Addition of Modified Pilates Exercises to a Minimal Intervention in Patients with Chronic Low Back Pain: A Randomized Controlled Trial” ( Physical Therapy , 2013: 309–321) reported on an experiment involving 86 subjects with nonspecific low back pain. The participants were randomly divided into two groups of equal size. The first group received just educational materials, whereas the second group participated in 6 weeks of Pilates exercises. The sample mean level of pain (on a scale from 0 to 10) for the control group at a 6-week follow-up was 5.2 and the sample mean for the treatment group was 3.1; both sample standard deviations were 2.3. a. Does it appear that true average pain level for the control condition exceeds that for the treatment condition? Carry out a test of hypotheses using a significance level of .01 (the cited article reported statistical significance at this a , and a sample mean difference of 2.1 also suggests practical significance). b. Does it appear that true average pain level for the control condition exceeds that for the treatment condition by more than 1? Carry out a test of appropriate hypotheses.

### Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

Chapter
Section

### Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809
Chapter 9.1, Problem 3E
Textbook Problem
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## Pilates is a popular set of exercises for the treatment of individuals with lower back pain. The method has six basic principles: centering, concentration, control, precision, flow, and breathing. The article “Efficacy of the Addition of Modified Pilates Exercises to a Minimal Intervention in Patients with Chronic Low Back Pain: A Randomized Controlled Trial” (Physical Therapy, 2013: 309–321) reported on an experiment involving 86 subjects with nonspecific low back pain. The participants were randomly divided into two groups of equal size. The first group received just educational materials, whereas the second group participated in 6 weeks of Pilates exercises. The sample mean level of pain (on a scale from 0 to 10) for the control group at a 6-week follow-up was 5.2 and the sample mean for the treatment group was 3.1; both sample standard deviations were 2.3.a. Does it appear that true average pain level for the control condition exceeds that for the treatment condition? Carry out a test of hypotheses using a significance level of .01 (the cited article reported statistical significance at this a, and a sample mean difference of 2.1 also suggests practical significance).b. Does it appear that true average pain level for the control condition exceeds that for the treatment condition by more than 1? Carry out a test of appropriate hypotheses.

a.

To determine

Whether the true average pain level for the control condition is greater than that of treatment condition.

### Explanation of Solution

Given info:

x¯=5.2, y¯=3.1, s1=2.3, s2=2.3, α=0.01, m=43, and n=43.

Calculation:

Here, μ1 represents the average pain level for control condition and μ2 represents the average pain level for treatment condition.

The test hypotheses are,

Null hypothesis:

H0:μ1=μ2

That is, the true average pain level for the control condition is same as treatment condition.

Alternative hypothesis:

Ha:μ1>μ2

That is, the true average pain level for the control condition is greater than that of treatment condition.

Test statistic:

Here, the sample size is large. That is, m>40 and n>40. Hence, the test statistic for the large samples is obtained as:

z=(x¯y¯)Δ0s12m+s22n

The difference between the mean pain level, Δ0=1

The test statistic value is obtained below:

z=(5.23.1)02.3243+2.3243=2.10.1230+0

b.

To determine

Whether the true average pain level for the control condition is more than 1 than that of treatment condition.

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